单面边坡的两种动力反应形式及其临界高度

Two patterns of dynamic responses of single-free-surface slopes and their threshold height

把单面边坡的动力反应分为高边坡动力反应和低边坡动力反应两类.研究了两种不同动力反应形式临界边坡高度的影响因素.量纲分析表明弹性条件下边坡动力反应临界高度Hthre与构成边坡材料的动弹性模量Ed的平方根成正比,与边坡材料的密度ρ成反比,与边坡动力输入的特征周期T成正比.结合弹性波动理论,利用大量数值模拟和统计分析得到了Hthre的表达式.当边坡的高度大于Hthre时,边坡的动力反应呈现高边坡动力反应规律,当边坡的高度小于Hthre时,边坡的动力反应呈现低边坡动力反应规律.

In this paper, the dynamic responses of slopes with single surface are grouped into two classes according to their distribution patterns, one is high slope dynamic response pattern and the other is low slope dynamic response pattern. Influence factors of the threshold height （ Hthre ） of the low slope response pattern and high slope response pattern are studied by dimensional analysis. The result shows that Hthre is proportional to square root of the dynamic elastic moduli Ed/p, meanwhile, it is proportional to period T of the dynamic input if slope material is under the elastic condition. Combined with the elastic wave propogation theory and large quantity of numerical simulations, formula of Hthre is derived by the statistic method. The formula tells that to a slope, if its height is larger than one fifth of the wavelength, its response will be the dynamic high slope effect. In contrary, its response will be the dynamic low slope effect.